For which value of x horizontal Tangent Line

1. Mar 30, 2008

chaosblack

For which value of x....horizontal Tangent Line

1. The problem statement, all variables and given/known data

For which value of x does f(x) = $$\frac{k}{ax^{2}+bx+c}$$ have a horizontal tangent line?

2. Relevant equations

Quotient Rule?

F'(x) = [g(x)a'(x) - a(x)g'(x)]/g(x)^2?

3. The attempt at a solution

Am I supposed to just sub it into a quotient rule format, making the derivative equal to 0?

So it would look like

0 = 0 - (2ax + b)/[[ax$$^{2}$$+bx+c]$$^{2}$$]? (and then simplify of course?)

Last edited: Mar 30, 2008
2. Mar 30, 2008

Shooting Star

That's correct. But there are certain restrictions on the values of a, b, and c.

(Also, when there is only a constant in the numerator, like f(x) = k/g(x), then you can directly use f'(x) = k d/dx[1/(g(x)] = k[-g'(x)/[g(x)^2], which is nothing but the quotient rule in a lesser number of steps.)

3. Mar 30, 2008

chaosblack

okay thanks, so the answer would just be the derivative set equal to 0?

4. Mar 30, 2008

happyg1

yes it is

5. Mar 30, 2008

chaosblack

okay thanks alot